Hypoelliptic convolution equations in 𝐾’_{𝑝}, 𝑝>1

Abstract

We consider convolution equations in the space K p ′ , p > 1 {K’_p},p > 1 , of distributions which “grow” no faster than exp ⁡ ( k | x | p ) \exp (k|x{|^p}) for some constant k. Our main result is a complete characterization of hypoelliptic convolution operators in K p ′ {K’_p} in terms of their Fourier transforms.